The multi-leader-follower game is a particular subset of classical game theory. These models serve as an analytical tool to study the strategic behavior of individuals in a noncooperative manner. In particular, the individuals (players) are divided into two groups, namely the leaders and the followers, according to their position in the game. Mathematically, this leads to optimization problems with optimization problems as constraints. The challenge in leader-follower problems arise due to possible nonsmoothness in the constraints.

We derive the best response function of the follower which we regularize using a suitable smooth regularizer. We discuss existence of Nash equilibria of the smoothed problems and deduce a numerical algorithm based on the smooth formulation. We further present an update of the primal variables for efficient computation. Finally, we present numerical results to illustrate our approach and give an outlook to future research.